2023 AMC 8 Problems/Problem 6
Solution 1
First, let us consider the cases where is a base. This would result in the entire expression being . However, if is an exponent, we will get a value greater than . As is greater than and , the answer is .
~MathFun1000
Solution 2
The maximum possible value of using the digit . We can maximize our value by keeping the and together in one power. (Biggest with biggest and smallest with smallest) This shows ==. (Don't want cause that's ) It is going to be
~apex304 (SohumUttamchandani, wuwang2002, TaeKim, Cxrupptedpat, stevens0209 (editing))